Differentiation Year 2?

[brisk canopy]

I got to cosx=-2/3

But when I use cast I don't get the right answers for the points

[kindred depot]

it's 3cos3x

dy/dx = 3cos3x + 2
cos3x = -2/3

range is now
0 <= x <= 2pi

3x = arccos(-2/3)

3x = 2.300523983, 3.982661324
x = 0.7668413277, 1.327553775

[brisk canopy]

My values are different for 3x

@kindred depot I got 3x= 5.44, 0.28

[kindred depot]

inverse cos of -2/3 is definitely 2.3...

[brisk canopy]

Yeah

But negative -2/3

So don't we look at Sin and Tan on cast diagram

[kindred depot]

eek cast

i didn't use cast

[brisk canopy]

Formula for cos?

[kindred depot]

I just typed cos^-1(-2/3) into my calc

and then did

[brisk canopy]

Oh

[kindred depot]

2pi - principle solution = 2nd solution

[brisk canopy]

Bruh so you can't do cast

[kindred depot]

then odd multiplies add 2pi
even multiples add 2pi

[kindred depot]

you can, but I wouldn't know how because it's an objectively worse method

knowing the rules of how they repeat is much easier imo

[brisk canopy]

I have the graphics calculator so can draw graph to check

[kindred depot]

same

but again

it's slow

if you just know the rules

you can do anything

and for really random numbers it's hard

w a graph

[brisk canopy]

Ok but when I do cast for positive cos I get both the solutions

Even tho cos Invquestion is negative

[kindred depot]

cos(-x) = cos(x)

as a rule

because cos is an even function

[brisk canopy]

Oh ty I get it now

[kindred depot]

np

[brisk canopy]

Also in this example ; Y= 15/2 x 3 to power of 6x

Differentiate why does the 15/2 stay?

[whole lodge]

Why is the coefficient 3

Can u explain

[torpid pike]

When you differentiate sinkx, it becomes kcoskx where k is the number

[whole lodge]

Oh I see

I knew about the derivative of sin x being cos x but I didn't know about the other rule

[kindred depot]

d/dx of sinax
= acosax

[torpid pike]

yeah it’s only cosx because k is 1

So it just doesn’t get written

[whole lodge]

Kinda similar how the derivative of e^kx is ke^kx

[torpid pike]

Sorta

[whole lodge]

Ye

Makes sense

Wait

[kindred depot]

that comes from the chain rule

[torpid pike]

Yes

[whole lodge]

So

Does this only apply to

[torpid pike]

Chain rule

[whole lodge]

Cosine?

[kindred depot]

sin(-x) = -sin(x)

[torpid pike]

I just imagine the cast circle 😭

[whole lodge]

Ain't that where u bring the power down as the coefficient of the bracket and u reduce the power by 1, and u multiply by the derivative of the expression in the bracket

[whole lodge]

Okok

[torpid pike]

I know no one likes cast but it’s helpful

[kindred depot]

yes

[torpid pike]

Yes

[whole lodge]

Can u explain why with cos

[torpid pike]

cos is not chain rule

It’s just trig differentiation

[kindred depot]

wdym

[whole lodge]

Cos -x= cos x

But with sin

[kindred depot]

because cos is an even function

[brisk canopy]

Can someone help?

[whole lodge]

sin -x = - sin x

[kindred depot]

and sin is an odd function

@whole lodge

[torpid pike]

yes, or think about cast solution

[whole lodge]

ChIn rule

?

[kindred depot]

no

[whole lodge]

Is that within brackets

[brisk canopy]

Oh I don't know how to do that

[kindred depot]

for the reason I jsut gave

[whole lodge]

Wdym by odd

Function

I'm in year 10 ion know that

[torpid pike]

You know chain rule or no?

[whole lodge]

Ohh

Wait

This is

[brisk canopy]

not yet

[whole lodge]

Dy/dx less than or greater than 0

I know this

[torpid pike]

ah ok

[whole lodge]

It's in the fm curriculum

I learnt it

[kindred depot]

that's for a different thing

[whole lodge]

U sure

Cuz if the average gradient is above 0 the whole graph is increasing

[kindred depot]

I mean yeah

but how does that help at all

[whole lodge]

Cuz u know if the graph is decreasing or increasing

Ohh

I see what u mean

It doesn't apply to this

🤦‍♂️

Okok I see

[torpid pike]

oh this reminds me of the one to one or one to many function

That was a headache of a chapter

[whole lodge]

makes sense

now

@kindred depot Do u do further maths for a level

[kindred depot]

yes

[whole lodge]

Is it hard

U think

[kindred depot]

yes